MATHEMATICS 347 



Mexico in 1556 ; it also contains some six pages of algebra, 

 mostly on quadratic equations. 



An interesting report on the progress of the complete edition 

 of the works of Leibniz, which was undertaken by an Inter- 

 national Commission in 1907, is given by Erdmann (Sitzungsber. 

 Preuss. Akad., 1921, 1 14). So far the only published result has 

 been the first volume of a catalogue of the Leibniz MSS., of 

 which 100 copies were distributed among the libraries of the 

 world {e.g. the British Museum) in 1908. The second volume, 

 entrusted to the Paris Academie des Sciences, has not appeared. 

 Berlin has now undertaken the whole of the production, esti- 

 mated to occupy thirty-nine octavo volumes, of which the first, 

 containing non-scientific correspondence to 1676, is ready for 

 the press. 



A review of the work of Thomas Jan Stieltjes (1856-94) on 

 continued fractions and on the integrals associated with his 

 name is given by R. D. Carmichael {Bull. Amer. Math. Soc, 27, 

 1921, 170). 



Logic and the Theory of Aggregates.^ — ^The Monist (vol. 31, 

 July igzi, 4.2,7) contains a translation of a paper by M. Winter, 

 " On the Logical Introduction to the Theory of Functions," in 

 which the author attempts to appraise the value of the study 

 of logistics. 



E. L. Post {Amer. Journ. Math., 43, 1921, 163) writes on the 

 general theory of Elementary Propositions, expanding and 

 generalising the matter contained in vol, i., pt. i., sec. A, of 

 Whitehead and Russell's Principia Mathematica. 



L. E. J. Brouwer {Proc. Amst. Acad., 23, 1921, 949) deals 

 with an intuitional basis for the theory of aggregates ; H. 

 Weyl {Math. Zeitschr., 10, 192 1, 39), in a lecture given at the 

 Mathematical Colloquium at Zurich in 1920, describes his own 

 work and Brouwer's on this subject. 



Other papers in this division are by M. Pasch {Math. Zs., 11, 

 1 92 1, 124) on the origin of the number-concept, by C. Burali- 

 Forti {Rend. Lincei, 30 (i), 192 1, 175 ; 30 (2), 1921, 26) on real 

 numbers and by Brouwer {Proc. Amst. Acad., 23, 192 1, 955) on 

 the question whether every real number can be expressed as 

 a decimal. 



Algebra and Analysis. — J. H. M. Wedderburn {Trans. Amer. 

 Math. Soc, 22, 1921, 129) investigates division algebras, i.e. 

 linear associative algebras in which division is permissible by 

 every element except zero. 



A. McAulay {Proc. Roy. Soc, A. 99, 1921, 292) has a paper 

 on Multenions and their use in relativity theory. 



Sir Thomas Muir {Trans. Roy. Soc. S. Africa, 10, 1921, 21) 

 publishes a note on axi-symmetric orthogonants. 



M. Bocher applied the statical problem of the positions of 



